I had the same confusion until I read the proof, though maybe I missed something earlier too. This corresponds to the validity condition in the last section.

Both generals start with either 0 or 1, and the condition is that if both started with 0 (i.e., initially wanted to individually retreat), they should both output 0. Likewise for 1. The thing about Eve deciding which value the generals start with may also be confusing; a better way to think of it is that 'no matter what both generals start with, this validity condition holds'.